Fuzzy Testing for Regression Coefficient of Fuzzy Numbers

    Volume 41, Issue 1 (January 2013)

    ISSN: 0090-3973

    CODEN: JTEOAD

    Published Online: 11 December 2012

    Page Count: 6


    Chen, Cheng-Che
    Dept. of Marketing and Logistics Management, Far East Univ., Tainan,

    Lai, Chun-Mei
    Dept. of Marketing and Logistics Management, Far East Univ., Tainan,

    Sun, Wen-Chi
    Dept. of Marketing and Logistics Management, Far East Univ., Tainan,

    Dept. of Accountancy, National Cheng Kung Univ., Tainan,

    (Received 19 February 2012; accepted 3 July 2012)

    Abstract

    Statistical regression analysis is one of the important statistical methods and has been widely applied to different scientific areas. Classical regression analysis models are limited to crisp data. In practice, however, data are usually imprecise because data are difficult to measure precisely or data are determined subjectively. When dealing with fuzzy data, using classical regression analysis method to test the regression coefficient would be improper and lead to an incorrect decision. Regarding the topic of fuzzy regression analysis, most of the related literature focused on presenting methods of estimating regression coefficient in order to improve the ability of data interpreting. Unfortunately, those studies ignored the significance of the regression coefficient. That is, after constructing a fuzzy linear regression model, the regression coefficient must be tested as to whether they have the statistical meaning or not. The purpose of this paper is to develop a fuzzy testing method to test the regression coefficient with fuzzy data. Under the environment of crisp hypothesis, crisp critical value, and fuzzy data, the upper bound and lower bound of α-cuts of fuzzy testing statistics can be obtained based on α-cuts of fuzzy sets and extension principle. The membership function of fuzzy testing statistics can then be constructed. Finally, based on the membership function, a fuzzy testing method is developed to analyze those fuzzy data and further to make a statistical decision. Because the proposed testing method is based on membership function, when the data are crisp, the proposed approach can degenerate to the classical testing method.


    Paper ID: JTE20120037

    DOI: 10.1520/JTE20120037

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    Author
    Title Fuzzy Testing for Regression Coefficient of Fuzzy Numbers
    Symposium , 0000-00-00
    Committee E11